We describe polycatalytic assemblies, comprising one or two streptavidin molecules and two to six attached nucleic acid catalysts (deoxyribozymes), with phosphodiesterase activity. When exposed to a matrix covered at high densities with oligonucleotide substrates, these molecules diffuse through the matrix continuously cleaving the substrate at rates comparable to those of individual catalysts in solution. Rates of diffusion (movement), processivity, and resident times of assemblies can be controlled through the number of catalytic units and the length of substrate/product recognition regions. The assemblies were characterized at the ensemble level using surface plasmon resonance.